A new approach to state observation of nonlinear systems with delayed output

We have studied the problem of static competitive routing to parallel queues with polynomial link holding costs. We have established the uniqueness of the NE for a general topology with the BPR cost [22] and have obtained a simple relationship with the globally optimal solution. We have further obtained some explicit results for the special case of affine link costs. The results of this note should prove useful for the analysis of networks with source-determined routing, when the link cost functions can be approximated by polynomial (and in particular affine) costs of the type considered here. The fact that the NE was shown to be efficient under a class of nonlinear costs can be used as a starting point for designing pricing mechanisms so as to obtain a socially optimal use of the network. The existence of equivalent mathematical programs for certain mixed equilibrium traffic assignment problems, " Euro.like paradoxes of Nash equilibria for load balancing in distributed computer systems, " Proc. Abstract—This note presents a new approach for the construction of a state observer for nonlinear systems when the output measurements are available for computations after a non negligible time delay. The proposed observer consists of a chain of observation algorithms reconstructing the system state at different delayed time instants (chain observer). Conditions are given ensuring global exponential convergence to zero of the observation error for any given the delay in the measurements. The implementation of the observer is simple and computer simulations demonstrate its effectiveness .